Discrete-time variable structure control using recursive switching function

In this paper, a new discrete-time variable structure control method using a recursive switching function is developed. The motivation for developing this method stems from the fact that variable structure control implemented in discrete time can lose the invariant property. In the proposed method, the switching function is recursively computed, utilizing the current tracking error vector and the previous switching function value. Combining the recursive switching function with a reaching law using a saturation function, the proposed control method achieves robustness to uncertainties, including both parametric errors and external disturbances. Under the condition that bounded uncertainties are constant or slowly varying, the tracking error is nearly zero even if the switching function does not become zero, preserving the invariant property of variable structure control